Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1580 and 1585 the smallest integer that is 500860 that is divisible by both numbers.
Least Common Multiple (LCM) of 1580 and 1585 is 500860.
LCM(1580,1585) = 500860
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1580 and 1585. First we will calculate the prime factors of 1580 and 1585.
Prime Factorization of 1580
2 | 1580 |
2 | 790 |
5 | 395 |
79 | 79 |
1 |
Prime factors of 1580 are 2, 5,79. Prime factorization of 1580 in exponential form is:
1580 = 22×51×791
Prime Factorization of 1585
5 | 1585 |
317 | 317 |
1 |
Prime factors of 1585 are 5,317. Prime factorization of 1585 in exponential form is:
1585 = 51×3171
Now multiplying the highest exponent prime factors to calculate the LCM of 1580 and 1585.
LCM(1580,1585) = 22×51×791×3171
LCM(1580,1585) = 500860
Factors of 1580
List of positive integer factors of 1580 that divides 1580 without a remainder.
1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580
Factors of 1585
List of positive integer factors of 1585 that divides 1585 without a remainder.
1, 5, 317, 1585
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1580 and 1585, than apply into the LCM equation.
GCF(1580,1585) = 5
LCM(1580,1585) = ( 1580 × 1585) / 5
LCM(1580,1585) = 2504300 / 5
LCM(1580,1585) = 500860
(i) The LCM of 1585 and 1580 is associative
LCM of 1580 and 1585 = LCM of 1585 and 1580
1. What is the LCM of 1580 and 1585?
Answer: LCM of 1580 and 1585 is 500860.
2. What are the Factors of 1580?
Answer: Factors of 1580 are 1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580. There are 12 integers that are factors of 1580. The greatest factor of 1580 is 1580.
3. What are the Factors of 1585?
Answer: Factors of 1585 are 1, 5, 317, 1585. There are 4 integers that are factors of 1585. The greatest factor of 1585 is 1585.
4. How to Find the LCM of 1580 and 1585?
Answer:
Least Common Multiple of 1580 and 1585 = 500860
Step 1: Find the prime factorization of 1580
1580 = 2 x 2 x 5 x 79
Step 2: Find the prime factorization of 1585
1585 = 5 x 317
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 500860 = 2 x 2 x 5 x 79 x 317
Step 4: Therefore, the least common multiple of 1580 and 1585 is 500860.